Question

The graph of f(x) = (0.5) is replaced by the graph of g(x) = (0.5)x - k. If g(x) is obtained by shifting f(x) down by 3 units, then what is the value of k? A. k=-3 B. k=- 1/3 C. k=1/3 D. k= 3

Answer 1

Recall that the the vertical shifting of functions is associated with the numerical value that is added to the original one. A possitive value k will shift the function k units up, and a negativa value (or subtracting k) will move it vertically down k units.

If I understand correctly, you forgot to type an "x"in the original function f(x), which should read:

f(x) = 0.5 x

Correct?

The new graph is g(x) = 0.5 x - k which is obtained by shifting the original f(x) DOWN by 3 units.

In order to shift the graph of f(x) DOWN three units, we need to SUBTRACT 3 from f(x), leading to : 0.5 x - 3

Therefore, the value of "k"in the given g(x) = 0.5 x - k must be 3.

which agrees with the last option in your list (option D)